The Fundamentals of Particle Size Analysis by Transmission Fluctuation Spectrometry. Part 2: A Theory on Transmission Fluctuations with Combined Spatial and Temporal Averaging

Abstract

The extinction of radiation in suspensions is traditionally described by the Bouguer‐Lambert‐Beer law (BLBL). Based on a quasi‐continuum approach, the BLBL does not account for the discrete nature of particles or their spatial extension and arrangement. If an extinction measurement is made with a high spatial and temporal resolution, the transmitted intensity signal shows significant fluctuations. The strength of fluctuation is related to the physical properties of the suspension and the process of spatial and temporal averaging. Exploiting this connection, it is possible to calculate the particle size distribution and the particle concentration from transmission measurements. This second part provides an analytical solution for the description of transmission fluctuations in terms of the expectancy of the transmission square, including both variations of the beam diameter to particle diameter ratio and variation of the temporal resolution of the signal capture. The result also provides the basis for describing the transmission fluctuations for beams of variable diameter and allows to define a measurement volume for the case of focussed beams.

Particle analysis by transmission fluctuation spectrometry with temporal correlation in multiphase flow

“…Different techniques have been developed, according to the method of signal averaging (i.e. spatial averaging, temporal averaging and their combination) [1][2][3][4][5][6].…”